Stephanie is 28 years older than Jessica. Nine years ago, Stephanie was 5 times as old as Jessica. How old is Jessica now?
Solution: We can use the given information to write down two equations that describe the ages of Stephanie and Jessica. Let Stephanie's current age be $s$ and Jessica's current age be $j$ The information in the first sentence can be expressed in the following equation: $s = j + 28$ Nine years ago, Stephanie was $s - 9$ years old, and Jessica was $j - 9$ years old. The information in the second sentence can be expressed in the following equation: $s - 9 = 5(j - 9)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $j$ , it might be easiest to use our first equation for $s$ and substitute it into our second equation. Our first equation is: $s = j + 28$ . Substituting this into our second equation, we get the equation: $(j + 28)$ $-$ $9 = 5(j - 9)$ which combines the information about $j$ from both of our original equations. Simplifying both sides of this equation, we get: $j + 19 = 5 j - 45$ Solving for $j$ , we get: $4 j = 64$ $j = 16$.